Optimal Retirement Time and Consumption/Investment in Anticipation of a Better Investment Opportunity

Gyoocheol Shim 한국경영과학회 2014 Management Science and Financial Engineering Vol.20 No.2

We investigate an optimal retirement time and consumption/investment policy of a wage earner who expects to find a better investment opportunity after retirement by being freed from other work and participating fully in the financial market. We obtain a closed form solution to the optimization problem by using a dynamic programming method under general time-separable von Neumann-Morgenstern utility. It is optimal for the wage earner to retire from work if and only if his wealth exceeds a certain critical level which is obtained from a free boundary value problem. The wage earner consumes less and takes more risk than he would without anticipation of a better investment opportunity.

A SNOWBALL CURRENCY OPTION

GYOOCHEOL SHIM 한국산업응용수학회 2011 Journal of the Korean Society for Industrial and A Vol.15 No.1

I introduce a derivative called “Snowball Currency Option” or “USDKRWSnowball Extendible At Expiry KO” which was traded once in the over-the-counter market in Korea. A snowball currency option consists of a series of maturities the payoffs at which are like those of a long position in a put option and two short position in an otherwise identical call. The strike price at each maturity depends on the exchange rate and the previous strike price so that the strike prices are random and path-dependent, which makes it difficult to find a closed form solution of the value of a snowball currency option. I analyze the payoff structure of a snowball currency option and derive an upper and a lower boundaries of the value of it in a simplified model. Furthermore, I derive a pricing formula using integral in the simplified model.

일반적 효용함수 하에서 대출제약의 정도와 최적 소비 및 투자

심규철(Gyoocheol Shim) 한국경영과학회 2016 經營 科學 Vol.33 No.1

I study optimal consumption and investment choices of an infinitely-lived economic agent with a general time-separable von Neumann-Morgenstern utility under general borrowing constraints against future labor income. An explicit solution is provided by the dynamic programming method. It is shown that the optimal consumption and risky investment decrease as the borrowing constraints become stronger.

Reversible Job-Switching Opportunities and Portfolio Selection

Shim, Gyoocheol,Koo, Jung Lim,Shin, Yong Hyun Springer-Verlag 2018 Applied mathematics and optimization Vol.77 No.2

<P>We study an optimal job-switching and consumption/investment problem of an infinitely-lived economic agent who exhibits constant relative risk aversion. We consider two kinds of jobs, one of which allows the agent to receive higher income but makes him suffer higher level of utility loss than the other. The job-switching opportunities are reversible in the sense that one can move from the current job to the other at any time. We provide the closed form solution for the optimal job-switching and consumption/investment policies by using the dynamic programming approach, and show various properties of the solution. We compare the optimal consumption/investment policies to those without job-switching opportunities. As a special case of our problem, we also compare the solution in the case where the agent has a reversible retirement option with that in the case where he has an irreversible retirement option.</P>

Hierarchical Contract and Collusion

Hyeng Keun Koo,Gyoocheol Shim,Jaeyoung Sung 한국재무학회 2009 한국재무학회 학술대회 Vol.2009 No.08

We study a moral-hazard-based multi-agent contracting model where the agents have the chance of collusion. We argue that an hierarchical contract, where investors contract the top manager and the top manager contracts all middle managers, is a collusion proof contract, and show that it is more e±cient than the direct contract in the presence of collusion chance.

Hierarchical Contract, Firm Size, and Pay Sensitivity

Hyeng Keun Koo,Gyoocheol Shim,Jaeyoung Sung 한국재무학회 2007 한국재무학회 학술대회 Vol.2007 No.05

We present a moral-hazard-based hierarchical contracting model, where investors con- tract the top manager and the top manager contracts all middle managers. We compare e®ects of hierarchical contracting on managerial contract sensitivities with those of a di- rect contracting benchmark where investors directly contract all managers. We argue that under hierarchical contracting, the top manager shifts his compensation risk to middle man- agers by providing middle managers with higher-powered incentive contracts than would be desired by investors under direct contracting. It is striking that this top managerial risk- shifting behavior motivates investors to design the top managerial contract in such a way that the top-managerial hierarchical contract sensitivity approaches either the ¯rst best or zero, as the ¯rm size grows. However, under some reasonable conditions such as correlated managerial e®ort outcomes, the top managerial sensitivity quickly approaches zero as the ¯rm size increases, and consequently, the sensitivity for large ¯rms can be far lower than predicted by the standard agency theory. This result can serve as an explanation of widely observed ¯rm-size e®ects on CEO compensations, namely, lower pay sensitivities for large ¯rms than those for small ¯rms. We also argue that even when investors are risk-neutral and then individual performance outcomes of nonexecutive employees may be very weakly correlated to the total outcome of the ¯rm, company-wide bonus plans for nonexecutive employees can still be justi¯ed under hierarchical contracting.

Optimal Multi-Agent Performance Measures for Team Contracts

Hyeng Keun Koo,Gyoocheol Shim,Jaeyoung Sung 한국재무학회 2007 한국재무학회 학술대회 Vol.2007 No.04

We present a continuous-time contracting model under moral hazard with many agents. The principal contracts many agents as a team, and they jointly produce correlated outcomes. We show the optimal contract for each agent is linear in outcomes of all other agents as well as his/her own. The structure of the optimal contract strikingly reveals that the optimal aggregate performance measure in general can be orthogonally decomposed into two statistics: one is a sucient statistic, and the other a non-sucient statistic. As a consequence, the optimal aggregate performance measure in general is not a sucient statistic, unless the principal is risk neutral. We further discuss agents' optimal eort choices using a \quadratic-cost" example, which also strikingly suggests that team contracts sometimes provide lower-powered eort incentives than individually separate contracts do.

Optimal Portfolio, Consumption-Leisure and Retirement Choice Problem with a Cobb-Douglas Utility and a CES Utility

Kyoung Jin Choi,Gyoocheol Shim,Yong Hyun Shin 한국산업응용수학회 2005 한국산업응용수학회 학술대회 논문집 Vol.- No.-

We study the optimal portfolio, consumption-leisure, and retirement choice of an infinitely-lived economic agent with a Cobb-Douglas utility and a CES(Constant Elasticity of Substitution) utility. Different from the previous works in investment problems, particular aspects of our problem are that the utility level of the agent is determined by both consumption and leisure and that the agent has a retirement option which can be exercised optimally considering tradeoff between utility effect from leisure and wealth effect from labor. We show that the agent retires optimally if his wealth exceeds a certain critical level. A closed form solution can be provided by solving a free boundary value problem. In particular, the critical wealth level, the optimal consumption-leisure and portfolio policy are given in closed form.

The Effects of Monetary Policy under the Credit Scoring System : The Experience from Korea in the Early 2000s

Jaewoon Koo,Hoseong Moon,Gyoocheol Shim 한국경제연구학회 2010 Korea and the World Economy Vol.11 No.3

This paper investigates why an expansionary monetary policy was ineffective in mitigating the credit-rationing problem in Korean bank loan markets in the early 2000s. We focus on the strict regulation on capital adequacy and the sticky implementation of the credit scoring system to explain monetary policy ineffectiveness. In a theoretical model, we show that, if the supply of loans responds more sensitively to the credit score than the demand for loans, an expansionary monetary policy cannot resolve the credit rationing problem. By estimating a disequilibrium model for bank loans, we find that excess supply existed in bank loan markets in the early 2000s, and thus expansionary monetary policy did not help to reduce disequilibrium in loan markets. This finding implies that banks should adjust the critical credit rate as well as interest rates for the efficacy of monetary policy.

OPTIMAL CONSUMPTION/INVESTMENT AND LIFE INSURANCE WITH REGIME-SWITCHING FINANCIAL MARKET PARAMETERS

SANG IL LEE,GYOOCHEOL SHIM 한국산업응용수학회 2015 Journal of the Korean Society for Industrial and A Vol.19 No.4

We study optimal consumption/investment and life insurance purchase rules for a wage earner with mortality risk under regime-switching financial market conditions, in a continuous time-horizon. We apply the Markov chain approximation method and suggest an efficient algorithm using parallel computing to solve the simultaneous Hamilton-Jaccobi-Bellman equations arising from the optimization problem. We provide numerical results under the utility functions of the constant relative risk aversion type, with which we illustrate the effects of regime switching on the optimal policies by comparing them with those in the absence of regime switching.